Question

Two small spherical insulators separated by 2.5 cm, which is much greater than either of their diameters. Both carry positive charge, one +60.0 microCoulombs and the other +6.66 microCoulombs. A third positive charge remains at rest between the two spheres and along the line joining them. What is the position of this charged sphere?

Answer 1

1.875 cm from 60 microcoulomb charge.

Step-by-step explanation:

Let the third charge be Q. Let it be put at x distance from 60 micro coulomb charge for balance.

Force on this charge due to first charge

=
`(k*60*10^(-6)Q)/(x^2)`

Force on this charge due to second charge

=
`(k*6.66*10^(-6)Q)/((2.5-x)^2)`

Since both these forces are equal
`(k*60*10^(-6)Q)/(x^2)=(k*6.66*10^(-6)Q)/((2.5-x)^2)`

`(60)/(6.66) = (x^2)/((2.5-x)^2)`
`(x)/(2.5 -x) = (3)/(1)`

x = 1.875

1.875 cm from 60 microcoulomb charge.